Question

A senator wishes to estimate the proportion of United States voters who favor new road construction. What size sample should be obtained in order to be 90% confident that the sample proportion will not differ K from the true proportion by more than 4%? Round up to the nearest whole number

A. 11
B. 256
C. 846
D. 423

Answer 1

To estimate the proportion of US voters who favor new road construction with a 90% confidence level and a margin of error no greater than 4%, a sample size of 423 is needed. Therefore, the correct option is D.

Step-by-step explanation:

To determine the sample size required to estimate the proportion of United States voters who favor new road construction with a 90% confidence level and a margin of error no greater than 4%, we need to use the formula for sample size calculation:

n = (Z^2 * p * (1-p)) / E^2

where:

• n is the sample size

• Z is the z-value corresponding to the confidence level (for 90% confidence level, Z = 1.645)

• p is the estimated proportion (unknown, so we assume p = 0.5 for the maximum sample size)

• E is the margin of error (0.04 in this case)

Plugging in the values, we have:

n = (1.645^2 * 0.5 * (1-0.5)) / 0.04^2 = 423